@article{fdi:010071565,
  title = {{O}n the stochastic {SIS} epidemic model in a periodic environment},
  author = {{B}aca{\¨e}r, {N}icolas},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n the stochastic {SIS} epidemic model with a contact rate , a recovery rate , and a population size , the mean extinction time is such that converges to as grows to infinity. {T}his article considers the more realistic case where the contact rate is a periodic function whose average is bigger than . {T}hen converges to a new limit , which is linked to a time-periodic {H}amilton-{J}acobi equation. {W}hen is a cosine function with small amplitude or high (resp. low) frequency, approximate formulas for can be obtained analytically following the method used in {A}ssaf et al. ({P}hys {R}ev {E} 78:041123, 2008). {T}hese results are illustrated by numerical simulations.},
  keywords = {{EPIDEMIOLOGIE} ; {MODELISATION} ; {MODELE} {STOCHASTIQUE} ; {EXTINCTION} ; {EQUATION} {DE} {HAMILTON} {JACOBI}},
  booktitle = {},
  journal = {{J}ournal of {M}athematical {B}iology},
  volume = {71},
  numero = {2},
  pages = {494--511},
  ISSN = {0303-6812},
  year = {2015},
  DOI = {10.1007/s00285-014-0828-1},
  URL = {https://www.documentation.ird.fr/hor/fdi:010071565},
}